Increase of dark energy with expansion of universe

[BillyT]

... Another related point. - going out on a limb here, the experts will catch me if I'm wrong:
The redshift we see from distant galaxies is not the same as the Doppler effect from a moving source. I picture it like this : as light travels across expanding space, "new space is created" continuously between each peak and trough of the traveling wave, so it gets gradually stretched out as it travels, hence increasing wavelength. The effect comes from what happens during the journey, not from how fast the distant object was moving when it emitted the light.

I'm 99.99% sure you are correct here; but part of the photons growing longer is that they: (1) may have originated in "deeper gravitation well" than the one the "fell into to be detected." & (2) Gravity is a force with infinite range (to speak of it as force created by mass) so the strength of the well they are "climbing out of" is not falling off just by inverse r^2 due to their speed of light travel away from their source, but the source is moving away from where they are at any instant too, making their separation from go as inverse R^2 where R is probably ever so slightly greater than the distance they have traveled (if gravity field is instantous at least.)

 

[wabbit]

I'm 99.99% sure you are correct here; but part of the photons growing longer is that they: (1) may have originated in "deeper gravitation well" than the one the "fell into to be detected."

Yes, this must play a role, as well as any proper motion of the source - but these are in addition to the expansion effect - and even if the photon comes from excited hydrogen emission of a small interstellar gas cloud at the confines of the galaxy (no deep well), I believe the redshift is pretty much the same, at least for distant galaxies where the expansion effect should dominate pretty much everything else - after all a recession velocity close to c is a big effect, we see gamma rays in the infrared I think for some very distant sources (hmm better check that one I pulled it out of a hat - edit : seems OK http://arxiv.org/abs/astro-ph/0502218).

 

[BillyT]

... But the point is "what is the velocity that goes into KE?". And it is not the recession velocity of comoving objects. ...

One does not need any point to be fixed, if LTE conditions apply, to define a temperature. It is the relative speeds, not absolute speed that define the total KE of an interacting system of stars (or the melting point of lead) - Those temperaturs do not depend upon the choice of frame. Lead melts at the same temperature in all frames.

If we assume that gravitational interactions have established LTE for the mater of the universe, then the KE in the definition of the universe's temperature is "frame invariant."

 

[wabbit]

You make me doubt, but if what you say is right then your KE involves supraluminal velocities, which sounds weird, does SR even allow that?

And are sure sure there is such a thing as the total KE of the universe? We know it isn't true for energy as a whole, but perhaps KE is OK, I don't know...

Edit:-not contesting your point for an interacting system, galaxy or such of course, but its applicability to global expansion.

Edit: I'm pretty sure I've stretched by limited understanding far enough here already if not too far, so I'll watch from the sidelines now and let more qualified posters bring us forward.

 

[BillyT]

You make me doubt, but if what you say is right then your KE involves supraluminal velocities, which sounds weird, does SR even allow that?

Yes SR even allows that. What you (or a particle) can not do is start at the origin of a coordinate system and then move away from that origin at greater than C.

Except perhaps in the first femto, femto seconds after the big bang, during the "expansion" - I don't know is C was a speed limit then.

 

[wabbit]

Yes SR even allows that. What you (or a particle) can not do is start at the origin of a coordinate system and then move away from that origin at greater than C.

I meant, applying the energy formula to compute KE with a supraluminal speed. Even with the GR formula this doesn't seem possible - OK this being clarified about what my question was, I will truly retreat and watch for a while.

 

[Phynos]

I'm 99.99% sure you are correct here; but part of the photons growing longer is that they: (1) may have originated in "deeper gravitation well" than the one the "fell into to be detected."

You seem to only be considering the time light spends escaping gravitational wells. Since the universe is highly homogeneous on large scales, we would expect that on average the energy lost by a photon due to it's motion out of a gravitational well will be countered by the energy gained by that same photon due to it's motion into a gravitational well. Gravitational red shift for the beginning of it's journey and blue shift for the end. So I don't think this can account for cosmological red shift.

 

[Nugatory]

The underlying problem here is that kinetic energy is, in general, only defined locally.

In a flat spacetime, we can choose the simultaneity convention that is under our noses (choose any inertial frame, use it to assign a $t$ coordinate to every event everywhere, declare all events with the same $t$ coordinate to be simultaneous) and we'll find that in that particular case we can extend our local frame everywhere and find that energy is globally conserved. In a curved spacetime, that trick doesn't work because there is no global inertial frame; we cannot use the coordinate velocities of objects to define a useful globally conserved quantity.